Cremona's table of elliptic curves

592 = 2⁴ · 37

Field	Data	Notes
Atkin-Lehner	2+ 37-	Signs for the Atkin-Lehner involutions
Class	592b	Isogeny class
Conductor	592	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	9472 = 28 · 37	Discriminant
Eigenvalues	2+  1  0  3  3  0  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-33,-85]	[a1,a2,a3,a4,a6]
j	16000000/37	j-invariant
L	1.9871937616075	L(r)(E,1)/r!
Ω	1.9871937616075	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	296b1 2368k1 5328e1 14800b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 592b1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	1	0	3	3	0	2	2	6	-2	4	-	7	-4	-1	9	-8	-4	-12	5	-13	10	1	-2	-12

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Quadratic twists for elliptic curve 592b1

-4	8	-3	5	-7	-11	13	37
296b1	2368k1	5328e1	14800b1	29008i1	71632b1	100048b1	21904a1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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